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Staircases play an essential role in crowd dynamics, allowing pedestrians to flow across large multi-level public facilities such as transportation hubs, and office buildings. Achieving a robust understanding of pedestrian behavior in these…

The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…

Analysis of PDEs · Mathematics 2025-09-17 Noureddine Igbida , Fahd Karami , Driss Meskine

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by partial…

Numerical Analysis · Mathematics 2020-06-04 Alessandro Alla , Caterina Balzotti , Maya Briani , Emiliano Cristiani

Crowd studies have gained increasing relevance due to the recurring incidents of crowd crush accidents. In addressing the issue of the crowd's persistent dynamism, this paper explored the macroscopic and microscopic features of pedestrians…

Physics and Society · Physics 2023-11-28 Jinghui Wang , Wei Lv , Huihua Jiang , Zhiming Fang , Jian Ma

In this article the dynamics of pedestrian streams in four different scenarios are compared empirically to investigate the influence of boundary conditions on it. The Voronoi method, which allows high resolution and small fluctuations of…

Physics and Society · Physics 2015-08-28 Jun Zhang , Armin Seyfried

Designing efficient traffic lanes for pedestrians is a critical aspect of urban planning as walking remains the most common form of mobility among the increasingly diverse methods of transportation. Herein, we investigate pedestrian counter…

Physics and Society · Physics 2020-04-10 Shihori Koyama , Daisuke Inoue , Akihisa Okada , Hiroaki Yoshida

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a…

Physics and Society · Physics 2024-02-02 Pedro Aceves-Sanchez , Rafael Bailo , Pierre Degond , Zoe Mercier

We study video crowd counting, which is to estimate the number of objects (people in this paper) in all the frames of a video sequence. Previous work on crowd counting is mostly on still images. There has been little work on how to properly…

Computer Vision and Pattern Recognition · Computer Science 2021-04-30 Haoyue Bai , S. -H. Gary Chan

Pedestrian detection in a crowd is a very challenging issue. This paper addresses this problem by a novel Non-Maximum Suppression (NMS) algorithm to better refine the bounding boxes given by detectors. The contributions are threefold: (1)…

Computer Vision and Pattern Recognition · Computer Science 2019-04-09 Songtao Liu , Di Huang , Yunhong Wang

Understanding crowd behaviors in a large social event is crucial for event management. Passive WiFi sensing, by collecting WiFi probe requests sent from mobile devices, provides a better way to monitor crowds compared with people counters…

Social and Information Networks · Computer Science 2020-02-12 Yuren Zhou , Billy Pik Lik Lau , Zann Koh , Chau Yuen , Benny Kai Kiat Ng

A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this…

Analysis of PDEs · Mathematics 2010-02-04 Bertrand Maury , Aude Roudneff-Chupin , Filippo Santambrogio

Short-range exposure to airborne virus-laden respiratory droplets is now acknowledged as an effective transmission route of respiratory diseases, as exemplified by COVID-19. In order to assess the risks associated with this pathway in…

Biological Physics · Physics 2022-08-08 Simon Mendez , Willy Garcia , Alexandre Nicolas

This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…

Statistical Mechanics · Physics 2022-11-11 Maria Bruna , Martin Burger , Jan-Frederik Pietschmann , Marie-Therese Wolfram

The fundamental diagram of pedestrian dynamics gives the relation between the density and the flow within a specific enclosure. It is characterized by two distinctive behaviors: the free-flow regime (for low densities) and the congested…

Physics and Society · Physics 2019-09-25 I. M. Sticco , G. A. Frank , F. E. Cornes , C. O. Dorso

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…

Numerical Analysis · Mathematics 2016-03-01 Gabriella Puppo , Matteo Semplice , Andrea Tosin , Giuseppe Visconti

Various methods to automate traffic data collection have recently been developed by many researchers. A macroscopic data collection through image processing has been proposed. For microscopic traffic flow data, such as individual speed and…

Computer Vision and Pattern Recognition · Computer Science 2016-09-09 Kardi Teknomo , Yasushi Takeyama , Hajime Inamura

We present one of the first comprehensive field datasets capturing dense pedestrian dynamics across multiple scales, ranging from macroscopic crowd flows over distances of several hundred meters to microscopic individual trajectories,…

Experimental results for congested pedestrian traffic are presented. For data analysis we apply a method providing measurements on an individual scale. The resulting velocity-density relation shows a coexistence of moving and stopping…

Physics and Society · Physics 2010-06-18 A. Seyfried , A. Portz , A. Schadschneider

Bridging the microscopic and macroscopic modelling scales in crowd dynamics constitutes an open challenge for systematic numerical analysis, optimization, and control. Here, we propose a manifold-informed machine learning approach to learn…

Machine Learning · Computer Science 2026-03-03 Hector Vargas Alvarez , Dimitrios G. Patsatzis , Lucia Russo , Ioannis Kevrekidis , Constantinos Siettos